scott - many thanks for your reply. Rather than re-install AWStats, though, I put a dirty hack in place. Every night after the update routine, I run a cron job which grabs the stats page via curl and saves it to the /stats directory as stats-MM-YY.htm where MM is the month and YY is the year.
This way, at the end of the month I'll have a full copy of that month's page and the new month's data will be written to stats-MM+1-YY.htm.
Not the most efficient routine, but it works!
Thanks to everyone for their help.